Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains
Complex Variables
2007-05-23 v4 Group Theory
Metric Geometry
Abstract
This paper lays down a foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL(2,R) group. We describe here geometries of corresponding domains. The principal role is played by Clifford algebras of matching types. Keywords: analytic function theory, semisimple groups, elliptic, parabolic, hyperbolic, Clifford algebras
Cite
@article{arxiv.math/0410399,
title = {Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains},
author = {Vladimir V. Kisil and Debapriya Biswas},
journal= {arXiv preprint arXiv:math/0410399},
year = {2007}
}
Comments
14 pages, AMS-LaTeX, 31 PS graphcs in 7 Figures; v2--the missing PS file is included now; v3 minor corrections, reference added; v4 numerous misprints corrected